Question:
Write a cosine function of the form f(t)= Acos(Bt) where A and B are real numbers that models the water level f(t) as a function of time measured in t hours since 8:30 a.m.
Answer:
The equation of the cosine function that models the water level as a function of time is;
Step-by-step explanation:
From the required equation, we have for a wave form
f(t) = A·cos(B·t)
A = Amplitude of the wave
B = The period of the wave
t = Time of wave
The period can be derived as follows
We have 7:30 to 1:00 is 5.5 hrs, therefore one full cycle occurs in 11 hours
The period is given by;
Therefore,
so that
The amplitude is given as the maximum displacement from the position at rest. Therefore, the amplitude = (15 - 7)/2 = 4 feet
Therefore the equation of the cosine function that models the water level as a function of time is;
.
The general equation for a line in the case where the slope and one point on the line are known is y-b = m(x-a), where m is the slope and (a,b) is the point.
Here f(4) = 3 corresponds to the point (4,3), and f '(4) = 2 corresponds to the slope of the tangent line at that point.
Thus the equation of the tangent line here is
y - 3 = 2(x - 4).
An alternative form of this equation would be y = 3 + 2x - 8, or
y = 2x - 5
Answer:
27,218
Step-by-step explanation:
After the first year, the population has grown by 4% of 17000, which is 0.04 times 17000 or 680. Therefore, the new population is 17000 + 680 or 17680.
After the second year, the population has grown by 4% of 17680, which is 0.04 times 17680 or 707.2. Of course, there's no such thing as 0.2 of a person, but we're just approximating, so that's ok. That brings the new total to 17680 + 707.2, which is 18387.2.
We could keep doing this for 12 years, but there's a shortcut. Since we're adding 4% each year, the new population is 104% of the old population. Therefore, we are multiplying by 104% each year. 104% is the same as 1.04. If we multiply 17000 by 1.04 12 times, we have something like this:
17000 * 1.04 * 1.04 * 1.04 * .... * 1.04
Another way to write that is using powers or:
17000 * 1.04^12
which gives us 27217.54, which we can round to 27,218 people.
688
x 29
6192
1376 x
19952
So you start by taking 9 from 29 and multiplying it by 688. when you get the answer put it below the line. then multiply the 2 from the 29 and whne you get the answer put a zero on the end and then add the answer you got from 9x688 (6192) and 2x688 (13760) and then thats youre answer. hope it helps!
Answer:
300
Step-by-step explanation:
every lamp can connect other lamps ，from the first ，it can connect the other 24 lamps，and then， the second ，can also connect other 24 。but the line between the first and the second is counted twice。
so it would be：
（1+2+3+...+24）×24÷2=300
